Which of the following numbers is a multiple of 13? ${46,60,62,65,111}$
Solution: The multiples of $13$ are $13$ $26$ $39$ $52$ ..... In general, any number that leaves no remainder when divided by $13$ is considered a multiple of $13$ We can start by dividing each of our answer choices by $13$ $46 \div 13 = 3\text{ R }7$ $60 \div 13 = 4\text{ R }8$ $62 \div 13 = 4\text{ R }10$ $65 \div 13 = 5$ $111 \div 13 = 8\text{ R }7$ The only answer choice that leaves no remainder after the division is $65$ $ 5$ $13$ $65$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $65$ $65 = 5\times13 13 = 13$ Therefore the only multiple of $13$ out of our choices is $65$. We can say that $65$ is divisible by $13$.